This relates generally to resonant inductive coupled communication systems.
Resonant inductive coupling (or electromagnetic induction) is the near-field wireless transmission of energy between two inductors (coils) between resonant circuits tuned to resonate at about the same frequency. The respective coils may exist as a single piece of equipment or include two separate pieces of equipment.
The general principle of energy transfer and efficiency for resonant inductive coupling is that if a given oscillating amount of energy (for example a pulse or a series of pulses) is forced into a primary (transmitting) coil which is capacitively loaded, the coil will “ring”, so that oscillating fields will occur, with the field energy transferring back and forth between the magnetic field in the inductor and the electric field across the capacitor at the resonant frequency. This oscillation will decrease (damp) over time at a rate determined by the gain-bandwidth (Q factor) of the resonant circuit, mainly due to resistive and radiative losses. However, provided the secondary (receiving) coil cuts enough of the magnetic field that it absorbs more energy than is lost in each cycle of the primary (transmitting) coil, then most of the transmitted energy can still be transferred.
The primary coil is generally the L part of a series RLC resonant circuit (resonant “tank”), and the Q factor for such a resonant tank is given by:
  Q  =            1      R        ⁢                  L        C            For example for R=20 ohm, C=1 μF and L=10 mH, Q=5. Because the Q factor for the resonant tank can be very high, only a small percentage of the magnetic field needs to be coupled from one coil to the other coil to achieve a reasonably high energy transfer efficiency, even though the magnetic field decays quickly with increasing distance from a coil, the primary coil and secondary coil can be several diameters apart. It can be shown that a figure of merit for the energy transfer efficiency (U) from primary coil and secondary coil is the following:U=k√{square root over (Q1Q2)}
Where k is the coupling coefficient, and Q1 and Q2 are the Q's for the primary (transmitting) tank and secondary (receiving) tank. Although assuming a reasonable k-value (k<1) the energy transfer efficiency for the resonant inductive coupled communication system can be high, the data rate may be limited because for a communication channel the maximum data-rate that can be achieved is limited by the channel's bandwidth, which is given by the Q of the tank (higher Q means a lower bandwidth). For example, for a tank tuned at 1 GHz with a Q of 10, the bandwidth is only 100 MHz. For example, for a binary modulation scheme (e.g., ON-OFF keying), the maximum data-rate is 2× the available bandwidth, governed by the well-known Nyquist theorem.